In topology preserving mapping, high-dimensional data is mapped onto a relatively low dimensional space such that the samples that are close to each other are mapped to nearby points and vice-versa. Topology preserving mapping can be used, for example, in visualization of the high-dimensional datasets. Also, in existing approaches, topology preserving mapping is usually performed in the Euclidian space or certain metric space. If the space is not Euclidian or a metric space, there is no such equivalent of topology preserving mapping. For example, in graphs, it may often be essential to know which nodes in the graph are very similar in nature and which are dissimilar.